Normal Map Bakes a Rainbow
Solved! For the sake of better organization, I had my high-poly meshes in a separate collection from my low-poly meshes.



In the Outliner window, I dragged the high-poly mesh into the same collection as the low-poly mesh, and after that the normal map baked properly (not perfectly, but it's at least a starting point.)

So I think what I'm missing is an understanding of what Collections are in Blender and how they are used; I was assuming they were a way to organize and collectively edit groups of objects in a scene (basically what it says on the tin), but evidently there's more to it than that.

(Haven't looked into details of why this worked yet, but it just bugs me when an op comes back with "solved!" but gives no explanation of how they solved it, so this is what I've got.)